I am going to guess Kansas in 88 is the only time. I looked up national Champs that came from the Big 6, 7, 8, 12, and 10. Not many teams from those conferences won championships. There may have been a non conference team we beat that went on to win.
Here are the champions from our conference
2007-08 Kansas (L 2 x)
1987-88 Kansas (1-1)
1951-52 Kansas (L 2 x)